1 files changed, 0 insertions, 395 deletions
diff --git a/vendor/golang.org/x/crypto/bn256/optate.go b/vendor/golang.org/x/crypto/bn256/optate.go
deleted file mode 100644
index 7ae0746..0000000
--- a/vendor/golang.org/x/crypto/bn256/optate.go
+++ /dev/null
@@ -1,395 +0,0 @@
-// Copyright 2012 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package bn256
-
-func lineFunctionAdd(r, p *twistPoint, q *curvePoint, r2 *gfP2, pool *bnPool) (a, b, c *gfP2, rOut *twistPoint) {
-	// See the mixed addition algorithm from "Faster Computation of the
-	// Tate Pairing", http://arxiv.org/pdf/0904.0854v3.pdf
-
-	B := newGFp2(pool).Mul(p.x, r.t, pool)
-
-	D := newGFp2(pool).Add(p.y, r.z)
-	D.Square(D, pool)
-	D.Sub(D, r2)
-	D.Sub(D, r.t)
-	D.Mul(D, r.t, pool)
-
-	H := newGFp2(pool).Sub(B, r.x)
-	I := newGFp2(pool).Square(H, pool)
-
-	E := newGFp2(pool).Add(I, I)
-	E.Add(E, E)
-
-	J := newGFp2(pool).Mul(H, E, pool)
-
-	L1 := newGFp2(pool).Sub(D, r.y)
-	L1.Sub(L1, r.y)
-
-	V := newGFp2(pool).Mul(r.x, E, pool)
-
-	rOut = newTwistPoint(pool)
-	rOut.x.Square(L1, pool)
-	rOut.x.Sub(rOut.x, J)
-	rOut.x.Sub(rOut.x, V)
-	rOut.x.Sub(rOut.x, V)
-
-	rOut.z.Add(r.z, H)
-	rOut.z.Square(rOut.z, pool)
-	rOut.z.Sub(rOut.z, r.t)
-	rOut.z.Sub(rOut.z, I)
-
-	t := newGFp2(pool).Sub(V, rOut.x)
-	t.Mul(t, L1, pool)
-	t2 := newGFp2(pool).Mul(r.y, J, pool)
-	t2.Add(t2, t2)
-	rOut.y.Sub(t, t2)
-
-	rOut.t.Square(rOut.z, pool)
-
-	t.Add(p.y, rOut.z)
-	t.Square(t, pool)
-	t.Sub(t, r2)
-	t.Sub(t, rOut.t)
-
-	t2.Mul(L1, p.x, pool)
-	t2.Add(t2, t2)
-	a = newGFp2(pool)
-	a.Sub(t2, t)
-
-	c = newGFp2(pool)
-	c.MulScalar(rOut.z, q.y)
-	c.Add(c, c)
-
-	b = newGFp2(pool)
-	b.SetZero()
-	b.Sub(b, L1)
-	b.MulScalar(b, q.x)
-	b.Add(b, b)
-
-	B.Put(pool)
-	D.Put(pool)
-	H.Put(pool)
-	I.Put(pool)
-	E.Put(pool)
-	J.Put(pool)
-	L1.Put(pool)
-	V.Put(pool)
-	t.Put(pool)
-	t2.Put(pool)
-
-	return
-}
-
-func lineFunctionDouble(r *twistPoint, q *curvePoint, pool *bnPool) (a, b, c *gfP2, rOut *twistPoint) {
-	// See the doubling algorithm for a=0 from "Faster Computation of the
-	// Tate Pairing", http://arxiv.org/pdf/0904.0854v3.pdf
-
-	A := newGFp2(pool).Square(r.x, pool)
-	B := newGFp2(pool).Square(r.y, pool)
-	C := newGFp2(pool).Square(B, pool)
-
-	D := newGFp2(pool).Add(r.x, B)
-	D.Square(D, pool)
-	D.Sub(D, A)
-	D.Sub(D, C)
-	D.Add(D, D)
-
-	E := newGFp2(pool).Add(A, A)
-	E.Add(E, A)
-
-	G := newGFp2(pool).Square(E, pool)
-
-	rOut = newTwistPoint(pool)
-	rOut.x.Sub(G, D)
-	rOut.x.Sub(rOut.x, D)
-
-	rOut.z.Add(r.y, r.z)
-	rOut.z.Square(rOut.z, pool)
-	rOut.z.Sub(rOut.z, B)
-	rOut.z.Sub(rOut.z, r.t)
-
-	rOut.y.Sub(D, rOut.x)
-	rOut.y.Mul(rOut.y, E, pool)
-	t := newGFp2(pool).Add(C, C)
-	t.Add(t, t)
-	t.Add(t, t)
-	rOut.y.Sub(rOut.y, t)
-
-	rOut.t.Square(rOut.z, pool)
-
-	t.Mul(E, r.t, pool)
-	t.Add(t, t)
-	b = newGFp2(pool)
-	b.SetZero()
-	b.Sub(b, t)
-	b.MulScalar(b, q.x)
-
-	a = newGFp2(pool)
-	a.Add(r.x, E)
-	a.Square(a, pool)
-	a.Sub(a, A)
-	a.Sub(a, G)
-	t.Add(B, B)
-	t.Add(t, t)
-	a.Sub(a, t)
-
-	c = newGFp2(pool)
-	c.Mul(rOut.z, r.t, pool)
-	c.Add(c, c)
-	c.MulScalar(c, q.y)
-
-	A.Put(pool)
-	B.Put(pool)
-	C.Put(pool)
-	D.Put(pool)
-	E.Put(pool)
-	G.Put(pool)
-	t.Put(pool)
-
-	return
-}
-
-func mulLine(ret *gfP12, a, b, c *gfP2, pool *bnPool) {
-	a2 := newGFp6(pool)
-	a2.x.SetZero()
-	a2.y.Set(a)
-	a2.z.Set(b)
-	a2.Mul(a2, ret.x, pool)
-	t3 := newGFp6(pool).MulScalar(ret.y, c, pool)
-
-	t := newGFp2(pool)
-	t.Add(b, c)
-	t2 := newGFp6(pool)
-	t2.x.SetZero()
-	t2.y.Set(a)
-	t2.z.Set(t)
-	ret.x.Add(ret.x, ret.y)
-
-	ret.y.Set(t3)
-
-	ret.x.Mul(ret.x, t2, pool)
-	ret.x.Sub(ret.x, a2)
-	ret.x.Sub(ret.x, ret.y)
-	a2.MulTau(a2, pool)
-	ret.y.Add(ret.y, a2)
-
-	a2.Put(pool)
-	t3.Put(pool)
-	t2.Put(pool)
-	t.Put(pool)
-}
-
-// sixuPlus2NAF is 6u+2 in non-adjacent form.
-var sixuPlus2NAF = []int8{0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1}
-
-// miller implements the Miller loop for calculating the Optimal Ate pairing.
-// See algorithm 1 from http://cryptojedi.org/papers/dclxvi-20100714.pdf
-func miller(q *twistPoint, p *curvePoint, pool *bnPool) *gfP12 {
-	ret := newGFp12(pool)
-	ret.SetOne()
-
-	aAffine := newTwistPoint(pool)
-	aAffine.Set(q)
-	aAffine.MakeAffine(pool)
-
-	bAffine := newCurvePoint(pool)
-	bAffine.Set(p)
-	bAffine.MakeAffine(pool)
-
-	minusA := newTwistPoint(pool)
-	minusA.Negative(aAffine, pool)
-
-	r := newTwistPoint(pool)
-	r.Set(aAffine)
-
-	r2 := newGFp2(pool)
-	r2.Square(aAffine.y, pool)
-
-	for i := len(sixuPlus2NAF) - 1; i > 0; i-- {
-		a, b, c, newR := lineFunctionDouble(r, bAffine, pool)
-		if i != len(sixuPlus2NAF)-1 {
-			ret.Square(ret, pool)
-		}
-
-		mulLine(ret, a, b, c, pool)
-		a.Put(pool)
-		b.Put(pool)
-		c.Put(pool)
-		r.Put(pool)
-		r = newR
-
-		switch sixuPlus2NAF[i-1] {
-		case 1:
-			a, b, c, newR = lineFunctionAdd(r, aAffine, bAffine, r2, pool)
-		case -1:
-			a, b, c, newR = lineFunctionAdd(r, minusA, bAffine, r2, pool)
-		default:
-			continue
-		}
-
-		mulLine(ret, a, b, c, pool)
-		a.Put(pool)
-		b.Put(pool)
-		c.Put(pool)
-		r.Put(pool)
-		r = newR
-	}
-
-	// In order to calculate Q1 we have to convert q from the sextic twist
-	// to the full GF(p^12) group, apply the Frobenius there, and convert
-	// back.
-	//
-	// The twist isomorphism is (x', y') -> (xω², yω³). If we consider just
-	// x for a moment, then after applying the Frobenius, we have x̄ω^(2p)
-	// where x̄ is the conjugate of x. If we are going to apply the inverse
-	// isomorphism we need a value with a single coefficient of ω² so we
-	// rewrite this as x̄ω^(2p-2)ω². ξ⁶ = ω and, due to the construction of
-	// p, 2p-2 is a multiple of six. Therefore we can rewrite as
-	// x̄ξ^((p-1)/3)ω² and applying the inverse isomorphism eliminates the
-	// ω².
-	//
-	// A similar argument can be made for the y value.
-
-	q1 := newTwistPoint(pool)
-	q1.x.Conjugate(aAffine.x)
-	q1.x.Mul(q1.x, xiToPMinus1Over3, pool)
-	q1.y.Conjugate(aAffine.y)
-	q1.y.Mul(q1.y, xiToPMinus1Over2, pool)
-	q1.z.SetOne()
-	q1.t.SetOne()
-
-	// For Q2 we are applying the p² Frobenius. The two conjugations cancel
-	// out and we are left only with the factors from the isomorphism. In
-	// the case of x, we end up with a pure number which is why
-	// xiToPSquaredMinus1Over3 is ∈ GF(p). With y we get a factor of -1. We
-	// ignore this to end up with -Q2.
-
-	minusQ2 := newTwistPoint(pool)
-	minusQ2.x.MulScalar(aAffine.x, xiToPSquaredMinus1Over3)
-	minusQ2.y.Set(aAffine.y)
-	minusQ2.z.SetOne()
-	minusQ2.t.SetOne()
-
-	r2.Square(q1.y, pool)
-	a, b, c, newR := lineFunctionAdd(r, q1, bAffine, r2, pool)
-	mulLine(ret, a, b, c, pool)
-	a.Put(pool)
-	b.Put(pool)
-	c.Put(pool)
-	r.Put(pool)
-	r = newR
-
-	r2.Square(minusQ2.y, pool)
-	a, b, c, newR = lineFunctionAdd(r, minusQ2, bAffine, r2, pool)
-	mulLine(ret, a, b, c, pool)
-	a.Put(pool)
-	b.Put(pool)
-	c.Put(pool)
-	r.Put(pool)
-	r = newR
-
-	aAffine.Put(pool)
-	bAffine.Put(pool)
-	minusA.Put(pool)
-	r.Put(pool)
-	r2.Put(pool)
-
-	return ret
-}
-
-// finalExponentiation computes the (p¹²-1)/Order-th power of an element of
-// GF(p¹²) to obtain an element of GT (steps 13-15 of algorithm 1 from
-// http://cryptojedi.org/papers/dclxvi-20100714.pdf)
-func finalExponentiation(in *gfP12, pool *bnPool) *gfP12 {
-	t1 := newGFp12(pool)
-
-	// This is the p^6-Frobenius
-	t1.x.Negative(in.x)
-	t1.y.Set(in.y)
-
-	inv := newGFp12(pool)
-	inv.Invert(in, pool)
-	t1.Mul(t1, inv, pool)
-
-	t2 := newGFp12(pool).FrobeniusP2(t1, pool)
-	t1.Mul(t1, t2, pool)
-
-	fp := newGFp12(pool).Frobenius(t1, pool)
-	fp2 := newGFp12(pool).FrobeniusP2(t1, pool)
-	fp3 := newGFp12(pool).Frobenius(fp2, pool)
-
-	fu, fu2, fu3 := newGFp12(pool), newGFp12(pool), newGFp12(pool)
-	fu.Exp(t1, u, pool)
-	fu2.Exp(fu, u, pool)
-	fu3.Exp(fu2, u, pool)
-
-	y3 := newGFp12(pool).Frobenius(fu, pool)
-	fu2p := newGFp12(pool).Frobenius(fu2, pool)
-	fu3p := newGFp12(pool).Frobenius(fu3, pool)
-	y2 := newGFp12(pool).FrobeniusP2(fu2, pool)
-
-	y0 := newGFp12(pool)
-	y0.Mul(fp, fp2, pool)
-	y0.Mul(y0, fp3, pool)
-
-	y1, y4, y5 := newGFp12(pool), newGFp12(pool), newGFp12(pool)
-	y1.Conjugate(t1)
-	y5.Conjugate(fu2)
-	y3.Conjugate(y3)
-	y4.Mul(fu, fu2p, pool)
-	y4.Conjugate(y4)
-
-	y6 := newGFp12(pool)
-	y6.Mul(fu3, fu3p, pool)
-	y6.Conjugate(y6)
-
-	t0 := newGFp12(pool)
-	t0.Square(y6, pool)
-	t0.Mul(t0, y4, pool)
-	t0.Mul(t0, y5, pool)
-	t1.Mul(y3, y5, pool)
-	t1.Mul(t1, t0, pool)
-	t0.Mul(t0, y2, pool)
-	t1.Square(t1, pool)
-	t1.Mul(t1, t0, pool)
-	t1.Square(t1, pool)
-	t0.Mul(t1, y1, pool)
-	t1.Mul(t1, y0, pool)
-	t0.Square(t0, pool)
-	t0.Mul(t0, t1, pool)
-
-	inv.Put(pool)
-	t1.Put(pool)
-	t2.Put(pool)
-	fp.Put(pool)
-	fp2.Put(pool)
-	fp3.Put(pool)
-	fu.Put(pool)
-	fu2.Put(pool)
-	fu3.Put(pool)
-	fu2p.Put(pool)
-	fu3p.Put(pool)
-	y0.Put(pool)
-	y1.Put(pool)
-	y2.Put(pool)
-	y3.Put(pool)
-	y4.Put(pool)
-	y5.Put(pool)
-	y6.Put(pool)
-
-	return t0
-}
-
-func optimalAte(a *twistPoint, b *curvePoint, pool *bnPool) *gfP12 {
-	e := miller(a, b, pool)
-	ret := finalExponentiation(e, pool)
-	e.Put(pool)
-
-	if a.IsInfinity() || b.IsInfinity() {
-		ret.SetOne()
-	}
-
-	return ret
-}